Logistic Regression and General Linear Models

Researchers working in broadly defined social sciences often have to deal with analyses in which the dependent variable is not a continuous variable defined on the interval scale. These are situations in which the dependent variable is either:

1. a binary variable, when respondents select one out of two options (e.g., whether they voted in the last election)
2. a nominal variable, when respondents select one out of three or more options (e.g., which party they voted for in the last election)
3. an ordinal variable (e.g., when a respondent chooses an answer on the Likert scale) or
4. a variable counting the number of occurrences of a phenomenon (e.g., how many times a respondent participated in protest actions).

For this type of dependent variable, it is not appropriate to use Ordinary Least Square (OLS) regression models but General Linear Models (GLMs), which are estimated in a different way from linear regression models.

Interpretation of GLMs is much more complex than for OLS models. Although GLMs are often used in social sciences, their use and correct interpretation still give researchers difficulties.

This course is an introduction to GLMs, and you will gain practical skills related to their use. But I will also introduce theoretical aspects of GLMs so you can understand and interpret them properly, and I will do it in a way that is understandable to those without rudimentary matrix algebra or calculus.

Day 1
The regression model with a binary dependent variable. We start by discovering why it is inappropriate to use OLS models in such cases; in particular, which OLS model assumptions are not met, and what might be the negative consequences of using OLS models for this type of data. Next, I will show you how to generalise a linear model so that it can be applied to models with a limited dependent variable. You will learn the linear predictor and the link function. We close with a presentation of Maximum Likelihood Estimation as a technique for estimating logistic regression model parameters.

Days 2 & 3
You will develop practical skills related to the interpretation of the binary logistic regression model, i.e. the interpretation of regression coefficients and odds ratios. I will present measures of goodness of fit of the models, and various versions of pseudo-R-squared measures. I demonstrate the extension of additive logistic regression models by introducing interactions between independent variables. You will learn how to correctly interpret a logistics binary regression model that incorporates interaction terms, and how to report the results using predicted probabilities, in particular through statistical graphics.

Day 4
Models with a nominal dependent variable, i.e. multinomial logistic regression.

Day 5
Techniques for an ordinal dependent variable, i.e. ordinal logistic regression, and regression models for counts. Poisson regression and negative binomial models.

I will illustrate the application of each method using analyses based on real-world data, presenting GLMs with their constraints and limitations.

By the end of the course, you will be able to:

• run GLMs on your own datasets
• interpret GLM regression coefficients and odds ratios
• assess the goodness of fit of the models
• estimate the uncertainty of predicted effects using simulations
• present the results using statistical graphics techniques.

You will be given assignments. Students who want ECTS credits must complete practical exercises related to the techniques introduced on a given day. You can use your own data for these (strongly recommended) or data provided by the instructor.

The lab session and assignments use the open-source statistical software R, enabling efficient implementation and advanced interpretation of GLMs. R’s graphical capabilities allow effective and relatively simple presentation of GLM results.

This is an advanced course. To get the most out of it, you should:

1. Understand the logic of inferential statistics 
   You should be familiar with hypothesis testing and concepts such as confidence intervals and significance level. If you are not, take course WB108 Introduction to Statistics for Political and Social Scientists or Introduction to Inferential Statistics: What you need to know before you take regression [link to 2018 course] at the 2019 ECPR Summer School. 
2. Be familiar with rudiments of the linear regression model estimated using the Ordinary Least Squares method 
   You should be familiar with the logic of linear regression analysis, assumptions of the linear regression model and regression with dummy variables. If you are not, take course WB107 Linear Regression with R/Stata: Estimation, Interpretation and Presentation or Multiple Regression Analysis: Estimation, Diagnostics, and Modelling [link to 2018 course] at the 2019 ECPR Summer School.
3. Have at least a basic understanding of the R language 
   You should be able to import into R a dataset written in the SPSS format and run a linear regression model. You should be able to conduct a set of basic data manipulations in R, such as: selecting observations, selecting variables and computing new variables using existing variables. If you are new to R, take course WA106A Introduction to R